Make the Crumble Topping: In a small bowl, mix flour, brown sugar, cinnamon, salt, and espresso powder. Add cold butter and work it in with a fork or fingertips until it forms small clumps. Refrigerate while you make the cookie dough.
Make the Cookie Dough: In a large bowl, cream together the butter, brown sugar, and granulated sugar until light and fluffy (2–3 minutes). Add egg yolk, pumpkin purée, vanilla, and espresso powder. Mix until smooth. In a separate bowl, whisk together flour, baking powder, baking soda, cinnamon, pumpkin pie spice, and salt. Add dry ingredients to wet and mix until combined. Dough will be soft.
Shape & Top: Preheat oven to 350°F (175°C). Line a baking sheet with parchment. Scoop dough into rounded tablespoons. Slightly flatten the tops and gently press a spoonful of crumble on each.
Bake: Bake for 10–12 minutes, or until edges are set and tops no longer look wet. Do not overbake.Cool on the pan for 5 minutes, then transfer to a wire rack.
Glaze: Whisk glaze ingredients until smooth and drizzle over cooled cookies.